Imagine you are tasked with designing a database system for a dynamic e$-$commerce platform that handles a vast amount of product data.

Based on the above scenario, answer the following:

Q$1)$ Describe the four key characteristics of databases and Database Management Systems $($DBMS$)$ while addressing how to efficiently structure data for products, customer information, and sales transactions incorporating key information models.

Q$2)$ Explore essential job roles for project success by clarifying their distinct responsibilities within the context of designing a dynamic e$-$commerce platform database system.

Q$3)$ Discuss the development of relations in database models, highlighting how the relational model accurately represents complex relationships and addressing challenges faced during implementation.